In this paper, we address bilevel multi-objective programming problems (BMPP) in which the decision maker at each level has multiple objective functions conflicting with each other. Given a BMPP, we show how to constr...In this paper, we address bilevel multi-objective programming problems (BMPP) in which the decision maker at each level has multiple objective functions conflicting with each other. Given a BMPP, we show how to construct two artificial multiobjective programming problems such that any point that is efficient for both the two problems is an efficient solution of the BMPP. Some necessary and sufficient conditions for which the obtained result is applicable are provided. A complete procedure of the implementation of an algorithm for generating efficient solutions for the linear case of BMPP is presented. A numerical example is provided to illustrate how the algorithm operates.展开更多
The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is signifi...The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty func- tion approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach.展开更多
In this paper,following the method of replacing the lower level problem with its Kuhn-Tucker optimality condition,we transform the nonlinear bilevel programming problem into a normal nonlinear programming problem with...In this paper,following the method of replacing the lower level problem with its Kuhn-Tucker optimality condition,we transform the nonlinear bilevel programming problem into a normal nonlinear programming problem with the complementary slackness constraint condition.Then,we get the penalized problem of the normal nonlinear programming problem by appending the complementary slackness condition to the upper level objective with a penalty.We prove that this penalty function is exact and the penalized problem and the nonlinear bilevel programming problem have the same global optimal solution set.Finally,we propose an algorithm for the nonlinear bilevel programming problem.The numerical results show that the algorithm is feasible and efficient.展开更多
In this paper, we focus on a class of nonlinear bilevel programming problems where the follower’s objective is a function of the linear expression of all variables, and the follower’s constraint functions are convex...In this paper, we focus on a class of nonlinear bilevel programming problems where the follower’s objective is a function of the linear expression of all variables, and the follower’s constraint functions are convex with respect to the follower’s variables. First, based on the features of the follower’s problem, we give a new decomposition scheme by which the follower’s optimal solution can be obtained easily. Then, to solve efficiently this class of problems by using evolutionary algorithm, novel evolutionary operators are designed by considering the best individuals and the diversity of individuals in the populations. Finally, based on these techniques, a new evolutionary algorithm is proposed. The numerical results on 20 test problems illustrate that the proposed algorithm is efficient and stable.展开更多
Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s f...Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s functions are convex if the follower＇s variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader＇s variable x, it is proved that the optimal solution y of the follower＇s mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower＇s programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.展开更多
The demand of hydrogen in oil refinery is increasing as market forces and environmental legislation, so hydrogen network management is becoming increasingly important in refineries. Most studies focused on single-obje...The demand of hydrogen in oil refinery is increasing as market forces and environmental legislation, so hydrogen network management is becoming increasingly important in refineries. Most studies focused on single-objective optimization problem for the hydrogen network, but few account for the multi-objective optimization problem. This paper presents a novel approach for modeling and multi-objective optimization for hydrogen network in refineries. An improved multi-objective optimization model is proposed based on the concept of superstructure. The optimization includes minimization of operating cost and minimization of investment cost of equipment. The proposed methodology for the multi-objective optimization of hydrogen network takes into account flow rate constraints, pressure constraints, purity constraints, impurity constraints, payback period, etc. The method considers all the feasible connections and subjects this to mixed-integer nonlinear programming （MINLP）. A deterministic optimization method is applied to solve this multi-objective optimization problem. Finally, a real case study is intro-duced to illustrate the applicability of the approach.展开更多
To solve the constraints of multi-objective optimization of the driver system and high nonlinear problems, according to the relevant dimensions of a car, we build a simulation model with Hybrid Ⅲ 50th dummy driver co...To solve the constraints of multi-objective optimization of the driver system and high nonlinear problems, according to the relevant dimensions of a car, we build a simulation model with Hybrid Ⅲ 50th dummy driver constraint system. The comparison of the driver mechanics index of the experimental data with the simulation data in the frontal crash shows that the accuracy of simulation model meets the requirements. The optimal Latin test design is adopted, and the global sensitivity analysis of the design parameters is carried out based on the Kriging model. The four most sensitive parameters are selected, and the parameters are solved by a multi-island genetic algorithm.And then the nonlinear programming quadratic line(NLPQL) algorithm is used to search for accurate optimization. The optimal parameters of the occupant restraint system are determined: the limiting force value of force limiter 2 985.603 N, belt extension 12.684%, airbag point explosion time 27.585 ms, and airbag vent diameter 27.338 mm, with the weighted injury criterion(WIC) decreased by 12.97%, the head injury decreased by 22.60%, and the chest compression decreased by 7.29%. The results show that the system integration of passive safety devices such as seat belts and airbags can effectively protect the driver.展开更多
This paper presents a modified method to solve multi-objective nonlinear programming problems with fuzzy parameters in its objective functions and these fuzzy parameters are characterized by fuzzy numbers. The modifie...This paper presents a modified method to solve multi-objective nonlinear programming problems with fuzzy parameters in its objective functions and these fuzzy parameters are characterized by fuzzy numbers. The modified method is based on normalized trade-off weights. The obtained stability set corresponding to α-Pareto optimal solution, using our method, is investigated. Moreover, an algorithm for obtaining any subset of the parametric space which has the same corresponding α-Pareto optimal solution is presented. Finally, a numerical example to illustrate our method is also given.展开更多
In [4], Fletcher and Leyffer present a new method that solves nonlinear programming problems without a penalty function by SQP-Filter algorithm. It has attracted much attention due to its good numerical results. In th...In [4], Fletcher and Leyffer present a new method that solves nonlinear programming problems without a penalty function by SQP-Filter algorithm. It has attracted much attention due to its good numerical results. In this paper we propose a new SQP-Filter method which can overcome Maratos effect more effectively. We give stricter acceptant criteria when the iterative points are far from the optimal points and looser ones vice-versa. About this new method, the proof of global convergence is also presented under standard assumptions. Numerical results show that our method is efficient.展开更多
文摘In this paper, we address bilevel multi-objective programming problems (BMPP) in which the decision maker at each level has multiple objective functions conflicting with each other. Given a BMPP, we show how to construct two artificial multiobjective programming problems such that any point that is efficient for both the two problems is an efficient solution of the BMPP. Some necessary and sufficient conditions for which the obtained result is applicable are provided. A complete procedure of the implementation of an algorithm for generating efficient solutions for the linear case of BMPP is presented. A numerical example is provided to illustrate how the algorithm operates.
基金supported by the National Science Foundation of China (70771080)Social Science Foundation of Ministry of Education (10YJC630233)
文摘The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty func- tion approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach.
基金Supported by the Key Project on Science and Technology of Hubei Provincial Department of Education (D20103001)
文摘In this paper,following the method of replacing the lower level problem with its Kuhn-Tucker optimality condition,we transform the nonlinear bilevel programming problem into a normal nonlinear programming problem with the complementary slackness constraint condition.Then,we get the penalized problem of the normal nonlinear programming problem by appending the complementary slackness condition to the upper level objective with a penalty.We prove that this penalty function is exact and the penalized problem and the nonlinear bilevel programming problem have the same global optimal solution set.Finally,we propose an algorithm for the nonlinear bilevel programming problem.The numerical results show that the algorithm is feasible and efficient.
文摘In this paper, we focus on a class of nonlinear bilevel programming problems where the follower’s objective is a function of the linear expression of all variables, and the follower’s constraint functions are convex with respect to the follower’s variables. First, based on the features of the follower’s problem, we give a new decomposition scheme by which the follower’s optimal solution can be obtained easily. Then, to solve efficiently this class of problems by using evolutionary algorithm, novel evolutionary operators are designed by considering the best individuals and the diversity of individuals in the populations. Finally, based on these techniques, a new evolutionary algorithm is proposed. The numerical results on 20 test problems illustrate that the proposed algorithm is efficient and stable.
基金supported by the National Natural Science Fundation of China (60374063)
文摘Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s functions are convex if the follower＇s variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader＇s variable x, it is proved that the optimal solution y of the follower＇s mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower＇s programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.
基金Supported by the National High Technology Research and Development Program of China （2008AA042902, 2009AA04Z162）, the Program of Introducing Talents of Discipline to University （B07031） and the National Natural Science Foundation of China （21106129）.
文摘The demand of hydrogen in oil refinery is increasing as market forces and environmental legislation, so hydrogen network management is becoming increasingly important in refineries. Most studies focused on single-objective optimization problem for the hydrogen network, but few account for the multi-objective optimization problem. This paper presents a novel approach for modeling and multi-objective optimization for hydrogen network in refineries. An improved multi-objective optimization model is proposed based on the concept of superstructure. The optimization includes minimization of operating cost and minimization of investment cost of equipment. The proposed methodology for the multi-objective optimization of hydrogen network takes into account flow rate constraints, pressure constraints, purity constraints, impurity constraints, payback period, etc. The method considers all the feasible connections and subjects this to mixed-integer nonlinear programming （MINLP）. A deterministic optimization method is applied to solve this multi-objective optimization problem. Finally, a real case study is intro-duced to illustrate the applicability of the approach.
基金Supported by Natural Science and Technology Research Project of the Jiangxi Education Department(GJJ202002, GJJ2202620)。
文摘To solve the constraints of multi-objective optimization of the driver system and high nonlinear problems, according to the relevant dimensions of a car, we build a simulation model with Hybrid Ⅲ 50th dummy driver constraint system. The comparison of the driver mechanics index of the experimental data with the simulation data in the frontal crash shows that the accuracy of simulation model meets the requirements. The optimal Latin test design is adopted, and the global sensitivity analysis of the design parameters is carried out based on the Kriging model. The four most sensitive parameters are selected, and the parameters are solved by a multi-island genetic algorithm.And then the nonlinear programming quadratic line(NLPQL) algorithm is used to search for accurate optimization. The optimal parameters of the occupant restraint system are determined: the limiting force value of force limiter 2 985.603 N, belt extension 12.684%, airbag point explosion time 27.585 ms, and airbag vent diameter 27.338 mm, with the weighted injury criterion(WIC) decreased by 12.97%, the head injury decreased by 22.60%, and the chest compression decreased by 7.29%. The results show that the system integration of passive safety devices such as seat belts and airbags can effectively protect the driver.
文摘This paper presents a modified method to solve multi-objective nonlinear programming problems with fuzzy parameters in its objective functions and these fuzzy parameters are characterized by fuzzy numbers. The modified method is based on normalized trade-off weights. The obtained stability set corresponding to α-Pareto optimal solution, using our method, is investigated. Moreover, an algorithm for obtaining any subset of the parametric space which has the same corresponding α-Pareto optimal solution is presented. Finally, a numerical example to illustrate our method is also given.
文摘In [4], Fletcher and Leyffer present a new method that solves nonlinear programming problems without a penalty function by SQP-Filter algorithm. It has attracted much attention due to its good numerical results. In this paper we propose a new SQP-Filter method which can overcome Maratos effect more effectively. We give stricter acceptant criteria when the iterative points are far from the optimal points and looser ones vice-versa. About this new method, the proof of global convergence is also presented under standard assumptions. Numerical results show that our method is efficient.
